differentiator is used in t.v.
phase shift in integrator is 180 degrees and phase shift in differentiator is 0 degrees
It doesn't. It can produce any waveform if you feed the integral of the desired waveform into the differentiator's input.
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noise is a ac signal(high frequency range), as LPF allows only lower frequencies integrator is has more noise immunity than differentiator
Finding the rate of change - in particular, the instantaneous rate of change.
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a phase shifted sine wave of a different amplitude.
A differentiator
Because the capacitor is in series with the output. Vice versa for the integrator.